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The Mathematica Guidebook for Programming [Hardcover]

Michael Trott
3.0 out of 5 stars  See all reviews (1 customer review)
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Book Description

28 Oct 2004 0387942823 978-0387942827 2004
This comprehensive, detailed reference provides readers with both a working knowledge of Mathematica in general and a detailed knowledge of the key aspects needed to create the fastest, shortest, and most elegant implementations possible. It gives users a deeper understanding of Mathematica by instructive implementations, explanations, and examples from a range of disciplines at varying levels of complexity. The three volumes -- Programming, Graphics, and Mathematics, total 3,000 pages and contain more than 15,000 Mathematica inputs, over 1,500 graphics, 4,000+ references, and more than 500 exercises.
This first volume begins with the structure of Mathematica expressions, the syntax of Mathematica, its programming, graphic, numeric and symbolic capabilities. It then covers the hierarchical construction of objects out of symbolic expressions, the definition of functions, the recognition of patterns and their efficient application, program flows and program structuring, and the manipulation of lists.
An indispensible resource for students, researchers and professionals in mathematics, the sciences, and engineering.

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Product details

  • Hardcover: 1072 pages
  • Publisher: Springer; 2004 edition (28 Oct 2004)
  • Language: English
  • ISBN-10: 0387942823
  • ISBN-13: 978-0387942827
  • Product Dimensions: 24.1 x 18.5 x 5.3 cm
  • Average Customer Review: 3.0 out of 5 stars  See all reviews (1 customer review)
  • Amazon Bestsellers Rank: 916,547 in Books (See Top 100 in Books)
  • See Complete Table of Contents

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From the reviews:

"This volume is the first one in a series of four books on the Mathematica programming language. It is best suited for those who … want to learn the sophisticated tricks of the advanced programming and to use Mathematica up to its full capacity. … The book addresses many features of human-computer interaction. … This book is one of the most valuable sources for the advanced users of Mathematica. … all the science/engineering/computer science/mathematics libraries should have this book and its companion volumes." (Matti Vuorinen, Zentralblatt MATH, Vol. 1080, 2006)

"The Mathematica GuideBook for Programming provided this reviewer with insights into solving and visualizing problems by using Mathematica … . Its wealth of exercises, annotated solutions and integrated bibliographic references should make this set a valuable part of the library of any Mathematica user. I highly recommend it." (Marvin Schaefer, MathDL, August, 2006)

"On the whole, the programming GuideBook provides a comprehensive, step-by-step development of Mathematica programming capabilities and contains an impressive collection of examples and worked exercises. Key Mathematica functions are discussed in detail, using interesting examples and put to the test in real programs." (Willy Hereman, SIAM Review, Vol. 47 (4), 2005)

Inside This Book (Learn More)
First Sentence
Although prior Mathematica knowledge is not needed to read The Mathematica GuideBook to Programming, it is assumed that the reader is familiar with basic actions in the Mathematica front end, including entering Greek characters using the keyboard, copying and pasting cells, and so on. Read the first page
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Front Cover | Table of Contents | Excerpt | Index | Back Cover
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Customer Reviews

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Most Helpful Customer Reviews
7 of 10 people found the following review helpful
Format:Hardcover|Verified Purchase
I bought this to replace the old copy of "Programming Mathematica" by Roman Maeder that I have - my copy is dated 1990, and is based on version 1.2 of Mathematica. Maeder's book assumes you have some idea of how to use Mathematica, and does not cover really basic stuff, but teaches you how to write packages (programs).
But this book really teaches nothing about programming like Maeder's old book does. I guess it was my fault - the title suggested something quite different to what it is to me.
This book will, if you read it carefully, teach you a lot of Mathematica. But starts with exactly the same example as Steven Wolfram's The Mathematica Book (the standard reference).
In[1]:= 1+1
Out[1]= 2
Much of the book is just the same sort of thing you find in the standard book (and is online at Wolfram Research's web site and is built into the help browser). I did not really want this book to be told how to take the sine of Pi/8 or other such material that is covered in The Mathematica Book.
This book is part of a 4-volume set. I only have this part and I somewhat doubt I'll buy any more. The book is quite heavy, but is significantly more manageable than Wolfram's book, which really is a pain because of its sheer size.
One thing I found odd about this book was the references. The preface has 59 references. Chapter 1 has 1194 references! Nobody could accuse the author of plagiarism! The book mentions that it took 20 years for astronomers to work out the tragectory of the moon, then cites about 10-15 journal references. Who would care? If I was an astronomer than perhaps I would, but I would not buy a book on Mathematica to learn about astronomy. I really was left puzzled what all the references achieved.
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Amazon.com: 4.3 out of 5 stars  11 reviews
50 of 50 people found the following review helpful
5.0 out of 5 stars Easily the best Mathematica reference I've seen 20 July 2005
By Zaeem Burq - Published on Amazon.com
Now then - one of the advantages of Mathematica is that it is supported by extensive documentation - both online and in print. Trott's Guidebooks (set of four books - Programming, Graphics, Symbolics and Numerics) is an impressive addition to this literature. These books stand out among the rest of the literature in several respects:

1. The whole set put together must be the biggest Mathematica book around.

2. The books teach Mahtematica through examples. But unlike most other books, the examples are not toy-examples; they are applications of Mathematica to non-trivial mathematical problems. Not only do they teach you Mathematica, they also teach you mathematics!!

3. The above mentioned non-trivial mathematical problems and results are very well referenced. Each chapter ends with an extensive bibliography - usually several hundred references. This further enhances the value of the Guidebooks as books on mathematics, not just Mathematica.

4. Each book comes with a DVD containing the WHOLE SET (yup - you heard it - all four books) as Mathematica notebooks. You can open these notebooks in Mathematica, edit them and experiment with them.

5. There is a piece of Mathematica code on the web-page that incorporates the whole set on DVD into the Mathematica help browser. This feature is just brilliant!!
40 of 40 people found the following review helpful
5.0 out of 5 stars Pedagogical masterpiece 5 Nov 2005
By Vijay Sonnad - Published on Amazon.com
I purchased the Programming Guidebook with considerable hesitation; to all appearances the Guidebooks are intended for the discerning cognoscenti, whereas I am very much a Mathematica novice.

The Programming Guidebook turned out to be a pleasant surprise: while there is a vast amount of material that would benefit the expert, it is also a careful and patient instruction book for the beginner.

Mathematica is a complex system; at first acquaintance it appears to be a bewildering collection of expressions and ad hoc programming styles. This book is a pedagogical masterpiece: it brings order to this seeming chaos by revealing the underlying framework. Topics are organized into comprehensible groups and the author focuses on each in detail.

Some parts that particularly appealed to this reader:

The section in Chapter 1 on Solutions to "What you always wanted to compute". This is a wonderfully whimsical list of problems that the author has gathered over many years and each is backed up by several references. This section is an unexpected delight and following up on the references provides an education in itself. The very first paragraph in Chapter 2, where the author provides one of the keys to unraveling Mathematica. The section in Chapter 3 on lambda calculus, which clarifies the use of pure functions. The entire collection of topics in Chapter 4 on meta-Mathematica.

Chapter 5 deals with the topic that is probably most foreign to those like myself used to traditional languages, (Fortran, C, C++); the treatment in this chapter is outstanding. Chapter 6 shows how Mathematica uses lists as a unified approach for vectors, matrices and tensors. Be aware however, that the book does require a fair background in mathematics or physics, (bachelor's or above).

It is clear that this is a labor of love; the author is deeply excited by the capabilities of Mathematica, and does his best to share his enthusiasm with the reader. The result is an inspiring book that is richly deserving of high praise. To fellow novices aspiring to use Mathematica gainfully, I can recommend the Programming Guidebook without hesitation. With study and patience, this Guidebook will dramatically enhance your ability to use Mathematica successfully.

I still believe my path to skillful use of Mathematica is going to be a long one, but it does not matter - with a guide like this, I expect to enjoy the journey immensely.
12 of 12 people found the following review helpful
5.0 out of 5 stars A Treasure of Mathematica Information 29 Dec 2005
By Paul B. Slater - Published on Amazon.com
Michael Trott's skill, knowledge and enthusiasm regarding the use of

Mathematica in scientific research is extraordinarily impressive, as I

have found to my considerable

benefit from some extended professional contact.

His infectious passion is manifested very strongly in this Guidebook

(devoted to programming, with the subsequent three volumes --- already

available --- being

concerned with the topics of graphics, symbolics and numerics).

Chapter 1 ("Introduction to Mathematica")

alone contains close to twelve hundred

references to the scientific literature (mostly physics, mathematics

and engineering

in nature), pertaining to one application or another --- many of an

engaging/intriguing nature.

Each chapter includes a set of exercises and a detailed solution

proposal for each exercise.

It certainly behooves each reader to peruse the Table of Contents and the

Index to find the topics of most interest to him or her. Much valuable time

for the computer practitioner

can certainly be spent with simple browsing of this impressive work of

devotion and erudition.

Desirably, some of the virtuosity in the use of Mathematica, abundantly

exhibited here by Trott, can be acquired by the reader.
8 of 8 people found the following review helpful
5.0 out of 5 stars A stunning triumph 14 Feb 2007
By Daniel M. Topa - Published on Amazon.com
Michael is a world authority on Mathematica. His deep insight, fresh perspectives and Herculean writing have produced a singular volume. It is impossible to turn the pages without a sense of amazement. If you want to appreciate the power and beauty of Mathematica, there is no better choice.

Here we see Mathematica as used by a master. The instruction is top notch, the examples are superlative, the topics are fascinating.

I think the customer rating system shows a blemish in allowing someone to rate this book as a poor introduction. It is a guidebook, a survey of capabilities, and as such is superlative example.
5 of 5 people found the following review helpful
5.0 out of 5 stars One of the most thorough books on ANY subject! 10 Jan 2008
By C. Bailey - Published on Amazon.com
Trott's 4 book set is an amazing achievement. The Programming volume is the most generally useful, and Trott suggests reading The Mathematica Book (by Wolfram) through, cover to cover, and then reading Trott's own books in the order Programming, Graphics, Numerics, Symbolics. So, start with Programming when reading Trott. I think following these instructions would be the best way to start from zero and master Mathematica.

It is hard to even consider all the information in here. I like areas others have discussed, like the Lambda calculus and the Metamathematica discussions. I also like that all 4 of the books are included, formatted as Mathematica Notebooks, on the DVD. The DVD that comes with any one volume contains that volume's notebooks already evaluated, and the other 3 volumes' notebooks unevaluated, and an unevaluated copy of that volume's notebooks, and the Table of Contents and Index and other infrastructural notebooks. So, while the hardcopy is very nice to have, I've also hunted around in the other volumes with great benefit.

It really makes no sense to compare these with Ruskeepaa's Mathematica Navigator, which is a nice example of the several books that help get one started with Mathematica. Trott is aiming at a whole different level. His explanations are more insightful, more complete. He discusses more topics.

Trott goes well beyond Wolfram's book. To quote him, "The four GuideBooks contain about 25,000 Mathematica inputs, representing more than 70,000 lines of commented Mathematica code. (For the reader already familiar with Mathematica, here is a more precise measure: The LeafCount of all inputs would be about 800,000 when collected in a list.) The GuideBooks also have more than 4,000 graphics, 100 animations, 8,000 references, and 1,000 exercises. More than 10,000 hyperlinked index entries and hundreds of hyperlinks from the overview sections connect all parts in a convenient way. The evaluated notebooks of all four volumes have a cumulative file size of about 10 GB."

Mathematica is a huge and powerful tool. As Mathematica is to other technical computing tools, Trott's set is to other Mathematica books.
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